Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
基本信息
- 批准号:RGPIN-2015-03747
- 负责人:
- 金额:$ 1.6万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2018
- 资助国家:加拿大
- 起止时间:2018-01-01 至 2019-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The lattice models of Statistical Mechanics have proved to be powerful tools for studying phase-change behaviour and equilibrium properties for polymers in solution. For such models, a polymer is considered to be any long chain molecule made of repeated units called monomers and a polymer chain is represented by a walk on a grid or lattice so that each monomer in the chain is one step apart from its neighbours. The resulting lattice polymer has flexibility (it can take on a variety of shapes) and the requirement that two monomers cannot be in the same location (the excluded volume effect) is easily incorporated. Although a highly simplified model, it is useful for predicting and understanding phenomena that result from the fact that polymers are large flexible molecules. At the same time, these models are of intrinsic mathematical interest due to the wealth of challenging open mathematical questions, many of which have arisen from polymer physics and more recently from molecular biology. For example, enzymes act on DNA to remove entanglements in order for normal cellular processes to proceed. To study this, a model in which two ends of a lattice polymer chain are joined into a ring can be used to represent the large-scale structure of the DNA molecule, and models of enzyme action on DNA have been developed by us. At the same time, there is interest in understanding the entanglement complexity of polymers confined in pores or capsids (such as DNA in a viral capsid) and also interest in determining the role of entanglements in polymer crystallization and polymer melts. For example, there are open questions about the relationship between how a polymer is packed in a capsid and its entanglement complexity, and for polymer melts, about the best approach for measuring the extent of entanglement. Lattice models for investigating these questions have also been developed by us. I plan to continue my research on lattice models of polymers using combinatorial analysis and computer simulations in order to better understand enzyme action on DNA and the entanglement complexity of confined polymers. The results will be of interest to molecular biologists and polymer chemists. In the case of enzyme action on DNA, an improved understanding of their action has the potential to impact Canadians by leading to improved cancer treatments. More generally, the results will add to our overall understanding of lattice models of polymers and phase transitions in polymer systems.
统计力学的晶格模型已被证明是研究聚合物在溶液中的相变行为和平衡性质的有力工具。对于这种模型,聚合物被认为是由称为单体的重复单元组成的任何长链分子,聚合物链由网格或晶格上的行走表示,因此链中的每个单体都与其相邻的单体相距一步。由此得到的晶格聚合物具有灵活性(它可以呈现各种形状),并且两个单体不能在同一位置的要求(排除的体积效应)很容易被纳入。虽然这是一个高度简化的模型,但它对于预测和理解由于聚合物是大的柔性分子这一事实而产生的现象很有用。与此同时,由于大量具有挑战性的开放数学问题,这些模型具有内在的数学兴趣,其中许多问题来自聚合物物理,最近来自分子生物学。例如,酶作用于DNA以消除缠结,从而使正常的细胞过程继续进行。为了研究这一问题,我们提出了一种晶格高分子链两端连接成环的模型来描述DNA分子的大尺度结构,并建立了酶作用于DNA的模型。与此同时,人们有兴趣了解限制在孔或衣壳中的聚合物(如病毒衣壳中的DNA)的纠缠复杂性,也有兴趣确定纠缠在聚合物结晶和聚合物熔体中的作用。例如,关于聚合物如何被包裹在衣壳中与其纠缠复杂性之间的关系,以及对于聚合物熔体,关于测量纠缠程度的最佳方法,还有一些悬而未决的问题。我们也发展了用于研究这些问题的格子模型。我计划利用组合分析和计算机模拟继续我对聚合物晶格模型的研究,以便更好地了解酶对DNA的作用和受限聚合物的纠缠复杂性。这一结果将引起分子生物学家和聚合物化学家的兴趣。就酶对DNA的作用而言,对其作用的更好理解有可能通过改进癌症治疗来影响加拿大人。更广泛地说,这些结果将增加我们对聚合物的晶格模型和聚合物体系中的相变的整体理解。
项目成果
期刊论文数量(0)
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会议论文数量(0)
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Soteros, Christine其他文献
Soteros, Christine的其他文献
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{{ truncateString('Soteros, Christine', 18)}}的其他基金
Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
- 批准号:
RGPIN-2020-06339 - 财政年份:2022
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
- 批准号:
RGPIN-2020-06339 - 财政年份:2021
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
- 批准号:
RGPIN-2020-06339 - 财政年份:2020
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
- 批准号:
RGPIN-2015-03747 - 财政年份:2019
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
- 批准号:
RGPIN-2015-03747 - 财政年份:2017
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
- 批准号:
RGPIN-2015-03747 - 财政年份:2016
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
- 批准号:
RGPIN-2015-03747 - 财政年份:2015
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice models of polymers: entanglement complexity and phase transitions
聚合物晶格模型:纠缠复杂性和相变
- 批准号:
46659-2010 - 财政年份:2014
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice models of polymers: entanglement complexity and phase transitions
聚合物晶格模型:纠缠复杂性和相变
- 批准号:
46659-2010 - 财政年份:2013
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
Lattice models of polymers: entanglement complexity and phase transitions
聚合物晶格模型:纠缠复杂性和相变
- 批准号:
46659-2010 - 财政年份:2012
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
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$ 1.6万 - 项目类别:
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$ 1.6万 - 项目类别:
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聚合物的晶格模型:纠缠复杂性和受限几何形状
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RGPIN-2020-06339 - 财政年份:2020
- 资助金额:
$ 1.6万 - 项目类别:
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Lattice Models of Polymers: Entanglement Complexity and Confined Geometries
聚合物的晶格模型:纠缠复杂性和受限几何形状
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RGPIN-2015-03747 - 财政年份:2019
- 资助金额:
$ 1.6万 - 项目类别:
Discovery Grants Program - Individual
The Statistical Mechanics of Lattice Models of Polymers
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